628 PROFESSOR CHRYSTAL ON THE DIFFERENTIAL TELEPHONE. 
In passing from I. to II. the intensity of all the tones of a composite sound 
are markedly increased ; but the increase is greater for the high tones, so that 
the quality is somewhat raised. 
When the capacity is very small, it is obvious beforehand that I. and III. 
would coimcide, and when it is very large, II. and III. would be identical. 
For intermediate capacities the effects are as follows :—For a certain capacity, 
in passing from I. to IIL, the high tones alone are increased in loudness, 
so that there is a rather marked raising of the quality; still on passing from 
II. to IIL. there is rather a lowering of the quality. When the capacity 
is greater, the sharpening effect is much greater, and, on account of contrast 
between high tones and low tones, it is more striking in passing from 
IJ. to III. than in passing from I. to III. When the capacity is still farther 
increased, it becomes difficult to distinguish between IT. and ITI. 
Experiment 8.—These results were much more marked when the primary 
coil was closed through the second coil of the differential telephone. On 
introducing a condenser with this arrangement the sound passed from a 
croak, croak, to a loud sharp tsi, tsa¢.* 
THEORY OF THE FOREGOING EXPERIMENTS. 
Experiment 1.—Denoting by &, &, £ the relative intensities (measured as 
above explained) in arrangements I., II., and III. of a note of frequency oath 
we get easily 
1 
{= (LEN FETS” 
Z 4 
& ~ (L+4N)n?+(R+ 28)?’ 
1 
&= S\2 
L+N)n?-+(R+5) 
Where L and R denote the coefficient of self-induction of the line and sender, 
N and § the self-induction and resistance of either coil of the differential tele- 
phone; the coefficient of mutual induction between the two coils is taken 
to be N. 
It is obvious at once that under all circumstances, for all tones, €&, > 1, in 
fact the effect of passing to III. is the same as if we halved the resistance 
of the receiver. 
* Tt is much to be desired that some of the above observations should be repeated by some one 
with a better ear for pitch than mine. I believe that very close accordance between theory and 
experiment would be brought out. I have not pushed either the theory or the experiments so far as I 
might have done, on account of my comparative obtuseness in the matter of pitch, 
